# if a `lt c lt b, ` then check the nature of roots of the equation <br> `(a -b)^(2) x^(2) + 2(a+ b - 2c)x + 1 = 0`

Updated On: 26-4-2021

4.8 k+

1.8 k+

Answer

Text Solution

Roots are non-real .

The discriminant of the given equation is <br>

D = 4 ( a + b - 2c)^(2) - 4(a - b)^(2)

<br>

= 4 (a + b - 2c - a b) ( a + b - 2c + a - b)

<br>

= 16 ( a - c) (b - c) lt 0 [because a lt c lt b]

<br> Hence, the roots of the given equation are complex.

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